An algebraic tool for obtaining conditional non-vanishing determinants

  • Authors:
  • Camilla Hollanti;Hsiao-Feng Lu;Roope Vehkalahti

  • Affiliations:
  • Department of Mathematics, University of Turku, Finland;Department of Communications Engineering, National Chiao Tung University, Hsinchu, Taiwan;Department of Mathematics, University of Turku, Finland

  • Venue:
  • ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
  • Year:
  • 2009

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Abstract

An algebraic tool from the theory of central simple algebras is proposed to obtain families of complex matrices satisfying the conditional non-vanishing determinant (CNVD) property. Such property is of great use in e.g. the design of multiuser space-time (ST) codes, in which context it is not always crucial for the transmission matrix to be invertible. On the other hand, whenever it is invertible, it is important that it has a nonvanishing determinant. Also any submatrix of any subset of users multiplied with its transpose conjugate should preferably have a non-vanishing determinant, provided it is non-zero. In recent submissions by Lu et al. it has been shown that, with suitable multiplexing, such property yields a construction of space-time codes that achieve the optimal diversity-multiplexing tradeoff (DMT) of the multiple-input multiple-output (MIMO) multiple access channel (MAC) and outperform the previously known ST codes.